In a state like Massachusetts, where the primary is open, what is a reason someone would enroll in a particular party? Do the national parties allocate money based on enrollment status in that state? Is there some other benefit besides declaring that you prefer one particular party?

If you're interested in participating in politics at a level higher than 'voting citizen', it helps to be enrolled in a party. It offers the opportunity to stand for office (and there are offices which are not hard to get-ward/precinct delegate to the state convention, for instance, which 'office' I have held). And generally you have to be enrolled in a party for more than a specific time (6 weeks, something like that), so enrolling just before the precinct caucus won't cut it.

Also, every year the parties hold caucuses in the towns. You can only participate in a caucus if you are a registered member of the party. The caucuses choose delegates to go to the annual state convention.

Now, in general the state conventions merely vote on party platform issues, but every four years the state convention chooses a candidate to endorse for governor. And that candidate usually ends up winning the primary, because they have the party's endorsement behind them. For example, both Shannon O'Brien and Deval Patrick were endorsed by the Democratic state conventions in their years of running for governor, and they both went on to win the primary.

(I've participated in Brookline's Democratic caucuses over the years, and also ran as an alternate delegate one year.)

Oh wait, that's different. That's still not whether or not they can vote at all (which in several states they still can't). Hm. I don't know when it changed. "Are listed as Unenrolled (formerly known as .Independent.)" My mom was registered as Independent 20 years ago, and in the sense of what's now unenrolled, not as a member of the Independent Party. I can't find when that changed.